Existence of an exotic crossed-product duality for every coaction

Let $(A,\delta)$ be a coaction of a locally compact group $G$. Say that $(A,\delta)$ satisfies $E$-crossed-product duality when

$$K_\delta=J_{\widehat\delta,E},$$

where $K_\delta$ is the kernel ideal of the Katayama duality map and $J_{\widehat\delta,E}$ is the ideal associated to the dual action. Every-coaction duality conjecture. Every coaction satisfies $E$-crossed-product duality for some $E$. The claim asks whether each coaction admits an exotic crossed-product level at which duality is restored; its status is not resolved in the supplied text.